Scores on a standard IQ test are normally distributed with population standard deviation 15.How many random IQ scores must be obtained if we want to find the true population mean (with an allowable error of 0.5)and we want 97% confidence in the results?
A)4,239
B)283
C)212
D)131
E)66

Question

Quizplus · Accepted Answer

To find the required sample size for estimating the population mean with a specific margin of error and confidence level, we use the formula for the sample size in estimating a mean with known population standard deviation: $n = \left(\frac{Z \cdot \sigma}{E}\right)^2$, where $Z$ is the Z-score corresponding to the desired confidence level, $\sigma$ is the population standard deviation, and $E$ is the allowable error (margin of error). For a 97% confidence level, the Z-score is approximately 2.17 (from Z-tables or a normal distribution calculator). Given $\sigma = 15$ and $E = 0.5$, we substitute these values into the formula: $n = \left(\frac{2.17 \cdot 15}{0.5}\right)^2 \approx 4239$.

Scores on a Standard IQ Test Are Normally Distributed with Population